Tooth surfaces of bevel and hypoid gears are usually finish ground using substantially the same manufacturing methods by which their tooth spaces were originally cut out of gear blanks. Of course, a grinding tool replaces a cutting tool when finish grinding the tooth surfaces, but otherwise, the machines and tooth generating operations used for cutting and grinding are very similar.
For example, grinding wheels used for finish grinding tooth surfaces are typically cup-shaped and have abrasive surfaces in the form of surfaces of revolution which are the same as the surfaces swept by cutting edges of gear cutting tools. The grinding wheels, like the comparable cutter tools, trace a substantially circular-arc tooth shape at each instant of their engagement with work gears. Tooth surfaces are generated in the work gears by rotating the grinding wheel (or cutting tool) about a machine cradle axis in a timed relationship with rotation of the work gear. The tool together with its relative motion represent a theoretical generating gear rolling through mesh with the work gear. Tooth surfaces of each tooth space are separately generated one at a time according to an intermittent indexing operation until all of the desired tooth surfaces are generated in the work gear.
It may be noted that this, the prevailing method, provides for rotating the grinding wheel at any desired grinding speed with respect to the work gear independently of the speed at which the grinding wheel is moved with respect to the work gear for generating tooth surfaces in the work gear. The rate at which the generating motions are applied may be controlled to optimize stock removal rates, and the path of the generating motions may be controlled to make desired adjustments to the geometry of tooth surfaces being generated.
However, it may be appreciated that in comparison to cutting operations in which tooth spaces are originally cut out of gear blanks, gear grinding operations require removal of a much smaller quantity of blank stock. Accordingly, it is possible to generate tooth surfaces much faster during grinding operations than during cutting operations. Nevertheless, the prevailing method requires a significant amount of time for repositioning the grinding wheel or cutter assembly with respect to the work gear between operations on adjacent tooth spaces. This loss of potentially productive time is particularly significant during grinding operations. In fact, as much as one-half of the time required to grind all of the desired tooth surfaces in a work gear may be spent performing these indexing operations during which the grinding wheel is not productively engaged with the work gear.
Another significant drawback of the prevailing method relates to difficulties with finish grinding gears which have tooth surfaces that have been previously cut using continuous indexing operations. Cutting tools used for continuous indexing operations include cutting blades which are arranged in groups for separately engaging tooth spaces in a gear blank. In addition to the generating motions described above for intermittent indexing operations, continuous indexing operations require the cutting tools to be rotated about their respective axes in a timed relationship with rotation of the work gears so that all of the tooth spaces in the work gears are generated by a single continuous generating motion.
In contrast to the circular arc tooth shape of bevel and hypoid gears produced by intermittent indexing operations, the longitudinal tooth shape cut by continuous indexing operations generally takes the form of a cycloid (e.g., an epicycloid or hypocycloid.) The cycloidal tooth shape departs from the circular arc tooth shape by a changing direction and amount of curvature. Accordingly, a cup-shaped grinding wheel or any other shape defined by a simple surface of revolution cannot be used in the same manner practiced by the prevailing intermittent indexing method to reproduce the cycloidal tooth shape of gears cut by continuous indexing operations.
U.S. Pat. No. 3,877,176 to Kotthaus discloses an alternative type of grinding tool that is intended for use with continuous indexing operations. The blades of a continuous indexing tool are replaced by pencil shaped grinding bodies which are rotated about their axes to perform individual grinding functions analogous to the cutting functions of blades in the cutting tool. Although it would be possible to closely approximate the cycloidal tooth shape with the grinding tool of Kotthaus, the grinding tool is regarded as being very complex, difficult to maintain at required accuracy, and prone to rapid wear during use.
Another known approach uses a tapered (or conical) grinding tool having a tooth shape similar to a tapered hobbing tool that is used for cutting out tooth spaces in a continuous indexing cutting operation. For example, U.S. Pat. No. 1,693,740 and German Patent 692,127 disclose respective hobbing and grinding tools which include stock-removing tooth surfaces in the form of one or more threads of a tapered worm gear. Generally, the worm tool tooth surfaces have evenly spaced straight profiles in one section similar to a gear rack. Tooth surfaces in a first member of a work gear pair (e.g., ring gear) are formed by feeding the tapered worm tool into mesh with the first member. Tooth surfaces of the second work gear member (e.g., pinion) are generated by imparting an additional relative rolling motion between a complementary worm tool and the second member. The additional relative motion presents the complementary worm tool to the second member in a manner representing the first member rolling through mesh with the second member.
This known method of cutting and grinding gears is believed to have originated with some of the earliest designs of hypoid gears as a modified form of worm gearing. Nowadays, other tooth shapes are preferred for hypoid gears and it is generally not possible to produce these shapes with the known tapered worm tools. Perhaps even more importantly, the tapered worm tools are known to exhibit unsatisfactory cutting and grinding performance. The smaller end of the tapered tool performs differently than the larger end of the tool resulting in uneven cutting and grinding performance over the length of the tool.
Other known attempts to finish grind gears previously cut by continuous indexing operations use intermittent indexing operations while imparting cyclical grinding wheel motions to approximate the cycloidal tooth form. One such attempt, disclosed in U.S. Pat. No. 1,830,971 to Taylor, provides for rocking a flared-cup or dish-shaped grinding wheel back and forth along a tooth space following the desired tooth contour. However, the grinding wheel remains only briefly in contact with any point along tooth length, and generating operations must be slowed considerably to generate a smooth tooth surface. In fact, this grinding process may be even more time consuming than the cutting process previously used to form the tooth spaces.
Another attempt to use cyclical grinding wheel motions to approximate the cycloidal tooth shape is disclosed in U.S. Pat. No. 4,378,660 to Wiener. A high speed elliptical orbital motion is imparted to a cup-shaped grinding wheel during an intermittent indexing operation. Although it would be possible to closely match the cycloidal tooth shape of certain gear designs, other designs may not be adequately matched. Any departure from the desired cycloidal tooth shape increases the amount of grinding stock that must be left by the cutting operation, thereby adversely affecting grinding time, and may compromise performance characteristics expected from the desired tooth design. Of course, since intermittent indexing is used, a significant portion of production time is lost to the indexing operations.
A different approach to finish grinding tooth surfaces in bevel and hypoid work gears from those described above (which have attempted to reproduce at least some of the characteristics of the cutting method used to form tooth spaces in the work gears) is disclosed in U.S. Pat. No. 4,799,337 to Kotthaus, British Patent Application 2 155 372 and German Patent Application 34 25 800. Instead of attempting to adapt gear cutting methodology to grinding, this different approach is similar to other known gear finishing operations such as lapping, shaving and burnishing wherein the finishing tool is designed as a mating gear. In fact, the underlying principles of the approach are perhaps best explained in U.S. Pat. No. 2,256,586 to Wildhaber for a variety of such finishing operations. The approach involves rotating a gear-shaped tool having tooth surfaces coated with a thin layer abrasive material in mesh with a work gear. More particularly, the tool takes a form of a hypoid gear having an axis of rotation that is offset from the axis of the work gear. The amount of offset and the rotational speeds of the tool and work gear are controlled to produce a desired amount of sliding between the surfaces of the tool and work gear.
This different approach is distinguished from the above-described grinding method using a tapered worm tool by providing for the tool to be designed as a mating gear to a work gear produced by any of the known cutting methods. Tooth surfaces of both members of a work gear set may be generated to desired shape by separately rotating the work gear members in mesh with respectively mating gear-shaped tools.
Two significant advantages may be noted of this different approach. First, the approach may be practiced independently of the type of method used to cut tooth spaces in work gear blanks. Second, the gear-shaped tool remains in continuous contact with the work gear throughout the entire grinding operation. The first-mentioned advantage renders the approach more versatile than other methods linked to particular cutting practices, and the second-mentioned advantage provides for a minimum amount of production time to finish grind tooth surfaces in the work gears.
Despite these known advantages, two controlling practical considerations are believed to have limited commercial acceptance of the approach. The first consideration relates to the design of the gear-shaped tool as a conjugate mating member of the work gear. Once the tool is made, little can be done in regard to the making of routine developmental changes to work gear geometry, e.g., to correct or modify tooth surfaces and their prospective contact characteristics with the work gear's actual mating gear member. For example, it is known from U.S. Pat. Nos. 2,256,586 and 4,799,337 to adjust the operating positions between the tool and work gear while they are being rotated together in the manner practiced on known gear lapping machines (i.e., "V and H" or vertical and horizontal movements between the members of gear set being lapped), but these adjustments produce inconsistent results and only limited types of changes to the work gear geometry. Changes made to the geometry of the gear-shaped tool to effect routine developmental changes to work gear geometry are difficult and very expensive to make. In addition to performing an operation to modify the gear-shaped tool geometry, the expensive abrasive material on the tooth surfaces of the tool must be removed either prior to or in the course of that operation, and a new layer of abrasive material must be applied to the modified surfaces of the tool.
The second practical consideration working against commercial acceptance of this approach relates to variations in the grinding characteristics of the gear-shaped tool throughout each tooth mesh with the work gear. The gear-shaped tool and the work gear, like any other mating gears, roll with each other along a path of contact. At each point along this path, a different instant line of contact is defined on the tooth surface of the work gear which tends to vary in length along the path of contact. Typically, the instant line of contact tends to shorten as the path of contact moves toward the perimeter of the work gear tooth surface.
In practice, the instant line of contact more closely resembles an elliptical area of contact due to stock allowances, but the point remains the same, namely, the instant contact characteristics between the gear-shaped tool and work gear tend to vary along the path of contact on each work gear tooth surface. Further, during much of the period of contact along each gear tooth surface, other work gear teeth may also be in contact with other abrasive tooth surfaces of the tool. These variations in the length of contact between gear teeth and number of gear teeth in contact throughout each mesh cycle produce significant variations in the grinding performance of the gear-shaped tool. Such variations may result in uneven wear over the abrasive tooth surfaces of the tool, in undesirable changes to work gear tooth surface geometry, and in undesirable variations in the finish (i.e., roughness) across the tooth surfaces.
Thus, although the approach of finish grinding bevel and hypoid gears with gear-shaped tools provides important advantages over the prevailing method of finish grinding gears, even more significant practical problems remain with implementing such an approach on a commercial basis. Further, it may be appreciated that these practical problems reflect and undesirable "trade off" with certain of the more important features and advantages of the prevailing method.
For example, the prevailing method provides much more flexibility for influencing desirable tooth contact characteristics and grinding conditions over tooth surfaces of work gears by controlling tooth surface generating motions independently of the rotational speed of the grinding tool. Unlike the known method for using gear-shaped grinding tools, the rotary sweep of the grinding wheel of the prevailing method only defines an instant line of contact with the work gear, and separate generating motions are used to define the remaining instant lines which complete the work gear tooth surfaces.
In contrast, the same relative rotational motion of the gear-shaped tool and work gear about their respective axes which is required for purposes of achieving a desired grinding speed is also the same motion which governs the rate at which successive instant lines are generated on the tooth surfaces of the work gear. It is known from the general machining art that generating rates of that magnitude are not conducive to good grinding conditions. In fact, such high generating rates may be considered orders of magnitude greater than preferred generating rates for optimizing grinding conditions.
It should be noted that before tooth generation can take place, the tool must be fed into engagement with the work gear. For example, U.S. Pat. No. 4,799,337 proposes a variety of such feed motions for moving a gear-shaped tool into operative engagement with a work gear, including one that corresponds to what would otherwise be a generating motion about a machine cradle axis of a conventional bevel and hypoid generating machine. However, all of these known feed motions merely provide for moving gear-shaped tools into desired operating positions with respect to work gears and do not significantly affect the rate at which successive instant lines are generated on the tooth surfaces of work gears. In fact, most, if not all, the instant lines of contact on the desired surface of the work gear are generated at a single feed position corresponding to a full depth of engagement between the known gear-shaped tools and work gears.
In view of the above discussion of the major known practices for finish grinding tooth surfaces of bevel and hypoid gears, it may be appreciated that no solution has been found which overcomes drawbacks of the prevailing method without compromising important features of that method which are believed to be at least partly responsible for the method having been successful for over sixty years.
Having set forth certain important problems of the prior art to be solved by the present invention, it is considered of further importance to note certain fundamental teachings of the art to more completely describe the state of the art in which the invention was made. Of particular importance to the present invention is the long-standing concept of a so-called "basic member." A good explanation of this concept by its author is found in U.S. Pat. No. 1,676,419 to Wildhaber.
A basic member may be defined as being one of a of a pair of complementary theoretical generating gears which are respectively conjugate to the members of a conjugate gear pair. By way of this definition, it is understood that two members of a gear pair are conjugate to each other if each member is respectively conjugate to one of a pair of complementary basic members. Complementary theoretical generating gears, and in particular, basic members may be understood to share the same tooth surfaces, opposite sides of which are regarded as the effective tooth surfaces of the respective complementary generating gears. The concept the basic member explains how tooth surfaces in a pair of work gears may be generated by tools representing theoretical generating gears.
In practice, however, respective tools and motions used to generate mating members of gear pairs depart slightly from the requirements of basic members. This departure in practice from the concept of the basic member has been necessitated for two reasons. First, gear members of a pair are usually designed to depart from conjugacy by a controlled amount of mismatch to accommodate tooth distortions under expected loads and to permit some adjustability in the mounting locations of the gear members. Second, inherent characteristics of the tooling used in certain generating operations precludes an exact representation of a basic member.
Nevertheless, the concept of the basic member continues to provide a sound theoretical basis which may be used to define appropriate motions for generating conjugate tooth surfaces in a pair of work gears. Basic members which are intended to generate tooth surfaces in a conjugate gear pair must fulfill two particular kinematic requirements. First, relative angular rotation of a basic member with respect to either member of the conjugate gear pair must define an instant axis of rotation coincident with the instant axis of rotation of the conjugate gear pair. Second, relative linear velocity of points of contact between the kinematic pitch surfaces of the basic member and either member of the conjugate gear pair (i.e., points on the instant axis) must be directed along the instant axis in a fixed ratio with the relative angular velocity along the instant axis matching a similar ratio of linear and angular velocities between the conjugate members. In other words, a basic member in mesh with either of a pair of conjugate gears must define the same "lead" (i.e., axial advance per radian of turning about instant axis) as the meshing pair of conjugate gears themselves.
In the case of bevel gear pairs, the relative linear velocity along the instant axis at points of contact on the instant axis is zero. Accordingly, it is possible to define a basic member of bevel gear pairs as another bevel gear having an appropriate number of teeth for a given pitch angle (i.e., angle between gear axis and instant axis) which defines an instant axis position coincident with the instant axis of the gear pair. However, hypoid gear pairs include axes which are offset with respect to each other resulting in a component of linear velocity along the instant axis of the pair. It is known that it is generally not possible to define a basic member as another hypoid gear matching the lead of a hypoid gear pair. Instead, the basic member must include a supplemental linear velocity with respect to the hypoid gear pair timed with its rotation. For example, a supplemental linear velocity may be applied along the axial of a basic member defining the basic member as a helicoidal segment.